Nonlinear extensions of the Dirac equation and their implications in Q.E.D

We investigate the influence of additional nonlinear terms in the Dirac Lagrangian on strongly bound electron states in heavy and superheavy atoms. Upper bounds for the coupling constants are deduced by comparison with precision spectroscopy data in Q.E.D. We demonstrate that nonlinear interactions may cause significant modifications of electron binding energies in superheavy quasiatomic systems which would not be visible in ordinary atomic physics measurements. (orig.)